6o8 SCIENCE PROGRESS 



velocities of the molecules are distributed at haphazard, subject 

 to the conditions (i) that the total kinetic energy is a given 

 constant T, and (2) that Boltzmann's function H has a value 



greater than its minimum. And we then prove that -3— is, 



under those circumstances, much more likely to be negative 

 than positive. That is true. But the initial values of the 

 variables having been once assumed, their values after any 

 time t are determinate functions of the initial values and of t. 

 The law of probabilities has nothing further to say in the 

 matter, but having fixed the initial values is fufichis officio. 



24. The error consists, as I maintain, after the manner that 

 men call heresy, in assuming the law of probabilities to have 

 continuous action, as though an independent haphazard dis- 

 tribution of the variables took place at every instant. If that 



d H 

 were the case, it is true that — j- would be on an average negative 



at every instant, and the motion could not be periodic. There 

 are, in fact, at the initial instant a great number, say n, of possible 

 states of the system, and as many possible determinate courses 

 for all subsequent time. By the way in which we make the 

 initial distribution, each of these n states, with its determined 

 course, is as likely to happen as any other. Further, as we 

 are in complete ignorance of the sequence of events in any one 

 of the n courses, it is true that, to our minds subjectively, 

 each state of the system is at every instant as probable as 

 any other. But this ignorance of ours would exist in fact 

 whether the motion be periodic or irreversible. We cannot 

 therefore argue from our ignorance of the courses that the 

 motion is irreversible. For this reason I think the usually 

 accepted proof is illogical. 



25. Further, the objection to the H Theorem, first made, I 

 believe, by Loschmidt, that if all the velocities were at any 

 instant reversed, the system would retrace its course, is, to 

 my mind, fatal to any theorem of irreversible motion in a 

 gas whose molecules are such as the kinetic theory assumes, 

 provided that the isolation of the system be complete. Of 

 course, if a fresh haphazard distribution took place at every 

 instant, as the theory requires, the Loschmidt objection would 

 fail altogether, for on reversal of the velocities the system 

 would not retrace its course. And any external disturbance, 



